A Fast and Robust Algorithm to Count Topologically Persistent Holes in Noisy Clouds

@article{Kurlin2014AFA,
  title={A Fast and Robust Algorithm to Count Topologically Persistent Holes in Noisy Clouds},
  author={V. Kurlin},
  journal={2014 IEEE Conference on Computer Vision and Pattern Recognition},
  year={2014},
  pages={1458-1463}
}
  • V. Kurlin
  • Published 5 December 2013
  • Computer Science
  • 2014 IEEE Conference on Computer Vision and Pattern Recognition
Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in noisy clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary contours when the cloud is analyzed at all possible scales. We design the algorithm to count holes that are most persistent in the filtration of offsets (neighborhoods) around given points. The input is a cloud of n points in the plane without any user-defined… 
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Three algorithms that solve the data skeletonisation problem for a general cloud with topological and geometric guarantees are compared and HoPeS represents the 1-dimensional shape of a cloud at any scale by the Optimality Theorem.
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    SGP '15
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TLDR
A homologically persistent skeleton is defined, which depends only on a cloud of points and contains optimal subgraphs representing 1‐dimensional cycles in the cloud across all scales, and is a universal structure encoding topological persistence of cycles directly on the cloud.
Research on a hole filling algorithm of a point cloud based on structure from motion.
TLDR
A fitting approach to fill the holes based on structure from motion (SFM) is proposed, which has been proven to be robust by experiments, and information of complex surface holes can be restored sufficiently.
Polygonal Meshes of Highly Noisy Images based on a New Symmetric Thinning Algorithm with Theoretical Guarantees
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A new symmetric thinning algorithms to extract from such highly noisy images 1-pixel wide skeletons with theoretical guarantees that establish the state-of-the-art in extracting optimal meshes fromhighly noisy images.
A higher-dimensional homologically persistent skeleton
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